If the orthocentre and the centroid of a triangle are at $(5,2,-6)$ and $(9,6,-4)$ respectively,then its circumcentre is

The incenter of the triangle $ABC$,whose vertices are $A(0,2,1)$,$B(-2,0,0)$,and $C(-2,0,2)$ is

Assertion $(A):$ If $(-1,3,2)$ and $(5,3,2)$ are respectively the orthocentre and circumcentre of a triangle, then $(3,3,2)$ is its centroid.
Reason $(R):$ Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio $1: 2$.
Which one of the following is true?

If a line makes angles $\alpha, \beta, \gamma, \delta$ with the four diagonals of a cube,then the value of $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma + \cos^2 \delta = $

If the ratio of the perpendicular distances of a variable point $P(x, y, z)$ from the $X$-axis and from the $YZ$-plane is $2:3$, then the equation of the locus of $P$ is

Let three points $A(2,3,4), B(3,4,2)$ and $C(4,2,3)$ in space be given. $A$ point $D$ in space is such that it is at a distance of $\sqrt{6}$ units from the $3$ given points. Then the volume of the tetrahedron $ABCD$ is -